Unit 5: Permutation, Combination and Probability - Practice Quiz

1 A student has 3 shirts and 2 pairs of trousers. How many different shirt-trouser outfits can the student wear?

2 A cafe offers 4 types of juice and 3 types of milkshake. If one drink is selected, how many choices are available?

3 In how many ways can 2 students be selected from a group of 4 students?

4 How many ways can one fruit be selected from 5 different fruits?

5 In how many ways can 3 different books be arranged in a row?

6 In how many ways can 2 different prizes be awarded to 2 students if each student receives one prize?

7 How many two-digit numbers can be formed using the digits 1, 2, and 3 without repetition?

8 How many one-digit even numbers can be formed using the digits 1, 2, 3, 4, and 5?

9 How many distinct arrangements can be made using all the letters of the word "CAT"?

10 How many distinct arrangements can be made using all the letters of the word "MOM"?

11 How many line segments are determined by 4 distinct points if no three points are collinear?

12 In how many ways can 4 people sit around a circular table?

13 What is the probability of a certain event?

14 What type of event has a probability equal to ?

15 A fair coin is tossed once. What is the probability of getting a head?

16 Two fair coins are tossed together. What is the probability of getting two tails?

17 A fair six-sided die is rolled once. What is the probability of obtaining an even number?

18 A fair six-sided die is rolled once. What is the probability of obtaining a number greater than 4?

19 One card is drawn from a standard deck of 52 cards. What is the probability of drawing an ace?

20 A card is known to be a face card from a standard deck. What is the probability that it is a king?

21 A security code consists of two distinct letters selected from 5 available letters, followed by three digits. Digits may be repeated. How many security codes are possible?

22 A committee of 5 is to be selected from 8 men and 6 women. In how many ways can the committee contain at least 3 women?

23 Seven distinct books are arranged on a shelf. If three particular mathematics books must remain together, how many arrangements are possible?

24 How many four-digit even numbers can be formed using the digits without repetition?

25 In how many distinct arrangements of the letters of the word EDUCATION do all five vowels occur together?

26 Ten points lie in a plane, with no three points collinear. How many triangles can be formed using these points as vertices?

27 Six people, including Arun and Beena, sit around a circular table. In how many arrangements are Arun and Beena not adjacent?

28 An integer is selected uniformly at random from to . What is the probability that it is divisible by or ?

29 One card is drawn from a standard deck. Let be the event that the card is a king and the event that it is a queen. How are and classified?

30 Four fair coins are tossed simultaneously. What is the probability of obtaining exactly two heads?

31 Two fair dice are rolled. What is the probability that at least one die shows a ?

32 One card is drawn from a standard deck of 52 cards. What is the probability that it is a red face card?

33 Two cards are drawn successively without replacement from a standard deck. Given that the first card is an ace, what is the probability that the second card is also an ace?

34 There are 4 routes from city to city and 3 routes from city to city . A traveler goes from to through and returns through without using either return route used on the outward journey. How many round trips are possible?

35 Four students are selected from a group of 10. If two particular students cannot both be selected, how many selections are possible?

36 Five boys and four girls are arranged in a row so that no two girls are adjacent. How many arrangements are possible?

37 How many four-digit odd numbers greater than can be formed using the digits without repetition?

38 How many distinct arrangements of the letters of BALLOON have the two letters L together?

39 Two cards are selected simultaneously from a standard deck. What is the probability that exactly one of them is an ace?

40 Factory supplies of a company's components and has a defect rate. Factory supplies and has a defect rate. If a selected component is defective, what is the probability that it came from factory ?

41 How many 8-character passwords can be formed using uppercase English letters and digits if the first character must be a letter, exactly two positions must contain distinct digits, and repetition of letters is allowed?

42 A committee of 5 is chosen from 7 men and 6 women. How many committees contain at least two women and do not contain both a particular man and a particular woman?

43 How many distinct arrangements of the letters of have no two 's adjacent?

44 How many 5-digit numbers with distinct digits are greater than and divisible by ?

45 How many distinct arrangements of the letters of have no two 's adjacent?

46 Eight points lie on a circle. Assuming no three chords meet at the same interior point, how many interior intersection points are formed by the chords joining pairs of points?

47 Eight distinct people are seated around a circular table. In how many arrangements, considered identical under rotation but not reflection, are two specified people not adjacent?

48 Two fair dice are rolled. What is the probability that their sum is prime and their product is even?

49 On a fair die, let be the event that the outcome is prime and the event that it is even. How should and be classified?

50 Five fair coins are tossed. Given that at least two heads occur, what is the probability of obtaining exactly three heads?

51 Three fair dice are rolled. What is the probability that the maximum is exactly and the sum is ?

52 A 5-card hand is dealt from a standard 52-card deck. What is the probability that it contains exactly two aces and at least one king?

53 An urn contains 5 red and 4 blue balls. Two balls are drawn without replacement. Given that at least one ball is red, what is the probability that both balls are red?

54 How many arrangements of the letters of have all five vowels nonadjacent and have appearing before ?

55 How many 5-digit numbers can be formed from the digits without repetition and are divisible by ?

56 In a convex polygon with vertices, how many ways can three diagonals be selected so that no two selected diagonals share an endpoint?

57 A fair die is rolled twice. Let be the event that the first result is even and the event that the second result is even. Which statement is correct?

58 Four fair coins are tossed. Given that the first and fourth coins show different results, what is the probability of obtaining at least two heads in total?

59 Two fair dice are rolled. Given that their sum is at least , what is the probability that they show the same number?

60 A 5-card hand is selected from a standard deck. Given that the hand contains at least one ace, what is the probability that it contains exactly two aces?